Subgroups — C₇×#34708 #13211924

Order 1792.

2548 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2481	C₂	1	2	yes	maximal, complemented
4	C₇×#2469	C₂	1	2	yes	maximal, complemented
5	C₇×#2458	C₂	1	2	yes	maximal, complemented
6	C₇×#2453	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2448	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2443	C₂	1	2	yes	maximal, complemented
9	C₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2426	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2421	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2416	C₂	1	1	yes	maximal, characteristic
14	C₇×#2409	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2398	C₂	1	2	yes	maximal, complemented
16	C₇×#2396	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#121	C₂	1	2	yes	maximal, complemented
21	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2290	C₂	1	2	yes	maximal, complemented
23	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
25	C₇×#529	—	2	8	no	—
26	C₂×C₇×#126	C₂²	1	2	yes	—
27	C₂×C₇×#125	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#124	C₂²	1	1	yes	characteristic
30	C₂×C₇×#123	C₂²	1	2	yes	—
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×#121	C₂²	1	1	yes	characteristic
34	C₂×C₇×#121	C₂²	1	1	yes	characteristic
35	C₂×C₇×#121	C₂²	1	2	yes	—
36	C₂×C₄×C₇×Q₈	—	2	8	no	—
37	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
38	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
41	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
49	C₂×C₇×#117	C₂²	1	2	yes	—
50	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
52	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₇	C₂²	1	2	yes	—
54	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
55	C₇×#400	C₂²	1	2	yes	—
56	C₇×#400	C₂²	1	2	yes	—
57	C₇×#400	C₂²	1	2	yes	—
58	C₇×#399	C₂²	1	2	yes	—
59	C₇×#398	C₂²	1	2	yes	—
60	C₇×#398	C₂²	1	2	yes	—
61	C₇×#397	C₂²	1	2	yes	—
62	C₇×#397	C₂²	1	2	yes	—
63	C₇×#396	C₂²	1	2	yes	—
64	C₇×#396	C₂²	1	2	yes	—
65	C₇×#395	C₂²	1	2	yes	—
66	C₇×#394	C₂²	1	2	yes	—
67	C₇×#394	C₂²	1	2	yes	—
68	C₇×#393	C₂²	1	2	yes	—
69	C₇×#393	C₂²	1	2	yes	—
70	C₇×#393	C₂²	1	2	yes	—
71	C₇×#391	C₂²	1	1	yes	characteristic
72	C₇×#391	C₂²	1	1	yes	characteristic
73	C₇×#391	C₂²	1	1	yes	characteristic
74	C₇×#391	C₂²	1	1	yes	characteristic
75	C₇×#390	C₂²	1	1	yes	characteristic
76	C₇×#390	C₂²	1	1	yes	characteristic
77	C₇×#390	C₂²	1	2	yes	—
78	C₇×#389	C₂²	1	1	yes	characteristic
79	C₇×#389	C₂²	1	1	yes	characteristic
80	C₇×#389	C₂²	1	1	yes	characteristic
81	C₇×#389	C₂²	1	1	yes	characteristic
82	C₇×#389	C₂²	1	2	yes	—
83	C₇×#388	C₂²	1	2	yes	—
84	C₇×#388	C₂²	1	2	yes	—
85	C₇×#388	C₂²	1	2	yes	—
86	C₇×#388	C₂²	1	2	yes	—
87	C₇×#388	C₂²	1	2	yes	—
88	C₇×#388	C₂²	1	2	yes	—
89	C₇×#388	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#387	C₂²	1	2	yes	—
92	C₇×#387	C₂²	1	2	yes	—
93	C₇×#387	C₂²	1	2	yes	—
94	C₇×#387	C₂²	1	2	yes	—
95	C₇×#386	C₂²	1	2	yes	—
96	C₇×#386	C₂²	1	2	yes	—
97	C₇×#386	C₂²	1	2	yes	—
98	C₇×#386	C₂²	1	2	yes	—
99	C₇×#386	C₂²	1	2	yes	—
100	C₇×#385	C₂²	1	2	yes	—
101	C₇×#385	C₂²	1	2	yes	—
102	C₇×#385	C₂²	1	2	yes	—
103	C₇×#382	C₂²	1	1	yes	characteristic
104	C₇×#380	C₂²	1	1	yes	characteristic
105	C₇×#380	C₂²	1	1	yes	characteristic
106	C₇×#380	C₂²	1	2	yes	—
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₇×#376	C₂²	1	2	yes	—
124	C₄³×C₇	C₂²	1	1	yes	characteristic
125	#34708	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂²×C₇×Q₈	—	2	4	no	—
127	C₂²×C₇×Q₈	—	2	4	no	—
128	C₂²×C₇×Q₈	—	2	4	no	—
129	C₂²×C₇×Q₈	C₂³	1	2	yes	—
130	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₇×D₄	C₂³	1	2	yes	—
133	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₇×D₄	C₂³	1	2	yes	—
135	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
145	C₇×#126	—	2	8	no	—
146	C₇×#125	—	2	4	no	—
147	C₇×#124	—	2	4	no	—
148	C₇×#124	—	2	4	no	—
149	C₇×#123	—	2	8	no	—
150	C₇×C₂²⋊Q₈	—	2	4	no	—
151	C₇×C₂²⋊Q₈	—	2	4	no	—
152	C₇×#121	—	2	8	no	—
153	C₇×#121	—	2	4	no	—
154	C₇×#121	—	2	4	no	—
155	C₄×C₇×Q₈	—	2	4	no	—
156	C₄×C₇×Q₈	—	2	4	no	—
157	C₄×C₇×Q₈	—	2	8	no	—
158	C₄×C₇×Q₈	—	2	4	no	—
159	C₄×C₇×Q₈	—	2	8	no	—
160	C₄×C₇×Q₈	D₄	1	8	yes	complemented
161	C₄×C₇×D₄	—	2	4	no	—
162	C₄×C₇×D₄	—	2	4	no	—
163	C₄×C₇×D₄	—	2	8	no	—
164	C₄×C₇×D₄	—	2	4	no	—
165	C₄×C₇×D₄	—	2	4	no	—
166	C₄×C₇×D₄	—	2	8	no	—
167	C₇×#117	—	2	8	no	—
168	C₂×C₇×C₄⋊C₄	—	2	4	no	—
169	C₂×C₇×C₄⋊C₄	—	2	8	no	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	—	2	4	no	—
213	C₂×C₄²×C₇	—	2	8	no	—
214	C₂×C₄²×C₇	—	2	4	no	—
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₇	C₂³	1	2	yes	—
224	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇	C₂³	1	2	yes	—
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	1	yes	characteristic
238	C₇×#95	C₂³	1	1	yes	characteristic
239	C₇×#95	C₂³	1	1	yes	characteristic
240	C₇×#95	C₂³	1	1	yes	characteristic
241	C₇×#95	C₂³	1	1	yes	characteristic
242	C₇×#95	C₂³	1	1	yes	characteristic
243	C₇×#95	C₂³	1	2	yes	—
244	C₇×#95	C₂³	1	2	yes	—
245	C₇×#95	C₂³	1	2	yes	—
246	C₇×#95	C₂³	1	2	yes	—
247	C₇×#95	C₂³	1	2	yes	—
248	C₇×#95	C₂³	1	2	yes	—
249	C₇×#95	C₂³	1	2	yes	—
250	C₇×#95	C₂³	1	2	yes	—
251	C₇×#95	C₂³	1	2	yes	—
252	C₇×#95	C₂³	1	2	yes	—
253	C₇×#95	C₂³	1	2	yes	—
254	C₇×#95	C₂³	1	2	yes	—
255	C₇×#95	C₂³	1	2	yes	—
256	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
257	C₂²×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
258	#2481	C₂×C₇	1	2	yes	complemented
259	#2469	C₂×C₇	1	2	yes	complemented
260	#2458	C₂×C₇	1	2	yes	complemented
261	#2453	C₂×C₇	1	1	yes	characteristic, complemented
262	#2448	C₂×C₇	1	1	yes	characteristic, complemented
263	#2443	C₂×C₇	1	2	yes	complemented
264	#2442	C₂×C₇	1	1	yes	characteristic, complemented
265	#2436	C₂×C₇	1	1	yes	characteristic, complemented
266	#2426	C₂×C₇	1	1	yes	characteristic, complemented
267	#2421	C₂×C₇	1	1	yes	characteristic, complemented
268	#2416	C₂×C₇	1	1	yes	characteristic
269	#2409	C₂×C₇	1	1	yes	characteristic, complemented
270	#2398	C₂×C₇	1	2	yes	complemented
271	#2396	C₂×C₇	1	2	yes	complemented
272	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
273	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
274	C₄×#121	C₂×C₇	1	2	yes	complemented
275	C₄×#121	C₂×C₇	1	1	yes	characteristic, complemented
276	#2295	C₂×C₇	1	1	yes	characteristic, complemented
277	#2290	C₂×C₇	1	2	yes	complemented
278	C₄²×D₄	C₂×C₇	1	1	yes	characteristic, complemented
279	C₂⁴×C₇	C₂⁴	1	2	yes	—
280	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₇×Q₈	—	2	32	no	—
283	C₂×C₇×Q₈	—	2	4	no	—
284	C₂×C₇×Q₈	—	2	2	no	—
285	C₂×C₇×Q₈	—	2	4	no	—
286	C₂×C₇×Q₈	—	2	4	no	—
287	C₂×C₇×Q₈	—	2	2	no	—
288	C₂×C₇×Q₈	—	2	2	no	—
289	C₂×C₇×Q₈	—	2	2	no	—
290	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
291	C₂×C₇×Q₈	#41	1	4	yes	—
292	C₂×C₇×D₄	—	2	2	no	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	2	4	no	—
295	C₂×C₇×D₄	—	2	4	no	—
296	C₂×C₇×D₄	—	2	4	no	—
297	C₂×C₇×D₄	—	2	4	no	—
298	C₂×C₇×D₄	—	2	4	no	—
299	C₂×C₇×D₄	—	2	2	no	—
300	C₂×C₇×D₄	—	2	2	no	—
301	C₂×C₇×D₄	—	2	2	no	—
302	C₂×C₇×D₄	—	4	2	no	—
303	C₂×C₇×D₄	#41	1	4	yes	—
304	C₂²×C₄×C₇	—	2	4	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	4	no	—
307	C₂²×C₄×C₇	—	2	2	no	—
308	C₂²×C₄×C₇	—	2	4	no	—
309	C₂²×C₄×C₇	—	2	2	no	—
310	C₂²×C₄×C₇	—	2	2	no	—
311	C₂²×C₄×C₇	—	2	2	no	—
312	C₂²×C₄×C₇	—	2	2	no	—
313	C₂²×C₄×C₇	—	2	4	no	—
314	C₂²×C₄×C₇	—	2	2	no	—
315	C₂²×C₄×C₇	—	2	4	no	—
316	C₂²×C₄×C₇	—	2	2	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	2	2	no	—
319	C₂²×C₄×C₇	—	2	4	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	2	2	no	—
322	C₂²×C₄×C₇	—	2	4	no	—
323	C₂²×C₄×C₇	—	2	2	no	—
324	C₂²×C₄×C₇	—	2	2	no	—
325	C₂²×C₄×C₇	—	2	4	no	—
326	C₂²×C₄×C₇	—	4	1	no	—
327	C₂²×C₄×C₇	—	4	1	no	—
328	C₂²×C₄×C₇	—	4	2	no	—
329	C₂²×C₄×C₇	#41	1	4	yes	—
330	C₂²×C₄×C₇	#41	1	4	yes	—
331	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
351	C₇×C₄⋊C₄	—	2	4	no	—
352	C₇×C₄⋊C₄	—	2	4	no	—
353	C₇×C₄⋊C₄	—	2	4	no	—
354	C₇×C₄⋊C₄	—	2	4	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	4	no	—
357	C₇×C₄⋊C₄	—	2	4	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	4	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	4	no	—
363	C₇×C₄⋊C₄	—	2	2	no	—
364	C₇×C₄⋊C₄	—	2	4	no	—
365	C₇×C₄⋊C₄	—	2	2	no	—
366	C₇×C₄⋊C₄	—	2	2	no	—
367	C₇×C₄⋊C₄	—	2	4	no	—
368	C₇×C₄⋊C₄	—	4	2	no	—
369	C₇×C₄⋊C₄	—	4	2	no	—
370	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
371	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	4	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	4	no	—
378	C₇×C₂²⋊C₄	—	2	4	no	—
379	C₇×C₂²⋊C₄	—	2	4	no	—
380	C₇×C₂²⋊C₄	—	2	4	no	—
381	C₇×C₂²⋊C₄	—	2	4	no	—
382	C₇×C₂²⋊C₄	—	2	4	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	4	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	—	2	4	no	—
387	C₇×C₂²⋊C₄	—	2	4	no	—
388	C₇×C₂²⋊C₄	—	2	4	no	—
389	C₇×C₂²⋊C₄	—	2	4	no	—
390	C₇×C₂²⋊C₄	—	2	4	no	—
391	C₇×C₂²⋊C₄	—	4	2	no	—
392	C₇×C₂²⋊C₄	—	4	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	4	no	—
396	C₄²×C₇	—	2	4	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	—	2	4	no	—
400	C₄²×C₇	—	2	2	no	—
401	C₄²×C₇	—	2	2	no	—
402	C₄²×C₇	—	2	2	no	—
403	C₄²×C₇	—	2	2	no	—
404	C₄²×C₇	—	2	2	no	—
405	C₄²×C₇	—	2	4	no	—
406	C₄²×C₇	—	2	2	no	—
407	C₄²×C₇	—	2	2	no	—
408	C₄²×C₇	—	4	1	no	—
409	C₄²×C₇	C₂×D₄	1	4	yes	—
410	C₄²×C₇	C₂×D₄	1	8	yes	—
411	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
412	#529	—	2	8	no	—
413	C₂×#126	C₂²×C₇	1	2	yes	—
414	C₂×#125	C₂²×C₇	1	1	yes	characteristic
415	C₂×#124	C₂²×C₇	1	1	yes	characteristic
416	C₂×#124	C₂²×C₇	1	1	yes	characteristic
417	C₂×#123	C₂²×C₇	1	2	yes	—
418	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
419	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
420	C₂×#121	C₂²×C₇	1	1	yes	characteristic
421	C₂×#121	C₂²×C₇	1	1	yes	characteristic
422	C₂×#121	C₂²×C₇	1	2	yes	—
423	C₂×C₄×Q₈	—	2	8	no	—
424	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
425	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
427	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
431	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
436	C₂×#117	C₂²×C₇	1	2	yes	—
437	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
439	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
440	C₂²×C₄²	C₂²×C₇	1	2	yes	—
441	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
442	#400	C₂²×C₇	1	2	yes	—
443	#400	C₂²×C₇	1	2	yes	—
444	#400	C₂²×C₇	1	2	yes	—
445	#399	C₂²×C₇	1	2	yes	—
446	#398	C₂²×C₇	1	2	yes	—
447	#398	C₂²×C₇	1	2	yes	—
448	#397	C₂²×C₇	1	2	yes	—
449	#397	C₂²×C₇	1	2	yes	—
450	#396	C₂²×C₇	1	2	yes	—
451	#396	C₂²×C₇	1	2	yes	—
452	#395	C₂²×C₇	1	2	yes	—
453	#394	C₂²×C₇	1	2	yes	—
454	#394	C₂²×C₇	1	2	yes	—
455	#393	C₂²×C₇	1	2	yes	—
456	#393	C₂²×C₇	1	2	yes	—
457	#393	C₂²×C₇	1	2	yes	—
458	#391	C₂²×C₇	1	1	yes	characteristic
459	#391	C₂²×C₇	1	1	yes	characteristic
460	#391	C₂²×C₇	1	1	yes	characteristic
461	#391	C₂²×C₇	1	1	yes	characteristic
462	#390	C₂²×C₇	1	1	yes	characteristic
463	#390	C₂²×C₇	1	1	yes	characteristic
464	#390	C₂²×C₇	1	2	yes	—
465	#389	C₂²×C₇	1	1	yes	characteristic
466	#389	C₂²×C₇	1	1	yes	characteristic
467	#389	C₂²×C₇	1	1	yes	characteristic
468	#389	C₂²×C₇	1	1	yes	characteristic
469	#389	C₂²×C₇	1	2	yes	—
470	#388	C₂²×C₇	1	2	yes	—
471	#388	C₂²×C₇	1	2	yes	—
472	#388	C₂²×C₇	1	2	yes	—
473	#388	C₂²×C₇	1	2	yes	—
474	#388	C₂²×C₇	1	2	yes	—
475	#388	C₂²×C₇	1	2	yes	—
476	#388	C₂²×C₇	1	2	yes	—
477	#387	C₂²×C₇	1	2	yes	—
478	#387	C₂²×C₇	1	2	yes	—
479	#387	C₂²×C₇	1	2	yes	—
480	#387	C₂²×C₇	1	2	yes	—
481	#387	C₂²×C₇	1	2	yes	—
482	#386	C₂²×C₇	1	2	yes	—
483	#386	C₂²×C₇	1	2	yes	—
484	#386	C₂²×C₇	1	2	yes	—
485	#386	C₂²×C₇	1	2	yes	—
486	#386	C₂²×C₇	1	2	yes	—
487	#385	C₂²×C₇	1	2	yes	—
488	#385	C₂²×C₇	1	2	yes	—
489	#385	C₂²×C₇	1	2	yes	—
490	#382	C₂²×C₇	1	1	yes	characteristic
491	#380	C₂²×C₇	1	1	yes	characteristic
492	#380	C₂²×C₇	1	1	yes	characteristic
493	#380	C₂²×C₇	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
500	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
503	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
504	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
506	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
507	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
509	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
510	#376	C₂²×C₇	1	2	yes	—
511	C₄³	C₂²×C₇	1	1	yes	characteristic
512	C₂³×C₇	—	2	1	no	—
513	C₂³×C₇	—	2	1	no	—
514	C₂³×C₇	—	2	1	no	—
515	C₂³×C₇	—	2	1	no	—
516	C₂³×C₇	—	2	1	no	—
517	C₂³×C₇	—	2	1	no	—
518	C₂³×C₇	—	2	1	no	—
519	C₂³×C₇	—	2	1	no	—
520	C₂³×C₇	—	2	1	no	—
521	C₂³×C₇	—	2	1	no	—
522	C₂³×C₇	—	2	2	no	—
523	C₂³×C₇	—	2	2	no	—
524	C₂³×C₇	—	2	2	no	—
525	C₂³×C₇	—	2	2	no	—
526	C₂³×C₇	—	2	2	no	—
527	C₂³×C₇	—	2	2	no	—
528	C₂³×C₇	—	2	2	no	—
529	C₂³×C₇	C₂×#41	1	2	yes	—
530	C₂³×C₇	C₂×#41	1	2	yes	—
531	C₂³×C₇	C₂×#41	1	2	yes	—
532	C₂³×C₇	C₂×#41	1	2	yes	—
533	C₂³×C₇	C₂⁵	1	1	yes	characteristic
534	C₇×Q₈	—	2	16	no	—
535	C₇×Q₈	—	2	8	no	—
536	C₇×Q₈	—	2	8	no	—
537	C₇×D₄	—	2	8	no	—
538	C₇×D₄	—	4	8	no	—
539	C₇×D₄	—	4	8	no	—
540	C₇×D₄	—	4	4	no	—
541	C₂×C₄×C₇	—	2	16	no	—
542	C₂×C₄×C₇	—	2	1	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	1	no	—
545	C₂×C₄×C₇	—	2	1	no	—
546	C₂×C₄×C₇	—	2	1	no	—
547	C₂×C₄×C₇	—	2	1	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	2	1	no	—
553	C₂×C₄×C₇	—	2	1	no	—
554	C₂×C₄×C₇	—	2	1	no	—
555	C₂×C₄×C₇	—	2	2	no	—
556	C₂×C₄×C₇	—	2	8	no	—
557	C₂×C₄×C₇	—	2	8	no	—
558	C₂×C₄×C₇	—	2	1	no	—
559	C₂×C₄×C₇	—	2	1	no	—
560	C₂×C₄×C₇	—	2	1	no	—
561	C₂×C₄×C₇	—	2	2	no	—
562	C₂×C₄×C₇	—	2	1	no	—
563	C₂×C₄×C₇	—	2	2	no	—
564	C₂×C₄×C₇	—	2	1	no	—
565	C₂×C₄×C₇	—	2	1	no	—
566	C₂×C₄×C₇	—	2	1	no	—
567	C₂×C₄×C₇	—	2	2	no	—
568	C₂×C₄×C₇	—	2	1	no	—
569	C₂×C₄×C₇	—	2	1	no	—
570	C₂×C₄×C₇	—	2	2	no	—
571	C₂×C₄×C₇	—	2	2	no	—
572	C₂×C₄×C₇	—	2	2	no	—
573	C₂×C₄×C₇	—	2	1	no	—
574	C₂×C₄×C₇	—	2	1	no	—
575	C₂×C₄×C₇	—	2	2	no	—
576	C₂×C₄×C₇	—	2	1	no	—
577	C₂×C₄×C₇	—	2	1	no	—
578	C₂×C₄×C₇	—	2	2	no	—
579	C₂×C₄×C₇	—	2	2	no	—
580	C₂×C₄×C₇	—	2	1	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	1	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	2	no	—
585	C₂×C₄×C₇	—	2	1	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	1	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	2	no	—
590	C₂×C₄×C₇	—	2	1	no	—
591	C₂×C₄×C₇	—	4	4	no	—
592	C₂×C₄×C₇	—	4	4	no	—
593	C₂×C₄×C₇	—	4	8	no	—
594	C₂×C₄×C₇	—	4	4	no	—
595	C₂×C₄×C₇	—	4	4	no	—
596	C₂×C₄×C₇	—	4	8	no	—
597	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
598	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
599	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
600	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
601	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₇	C₂×#41	1	2	yes	—
603	C₂×C₄×C₇	C₂×#41	1	2	yes	—
604	C₂×C₄×C₇	C₂×#41	1	4	yes	—
605	C₂×C₄×C₇	C₂×#41	1	2	yes	—
606	C₂×C₄×C₇	C₂×#41	1	2	yes	—
607	C₂×C₄×C₇	C₂×#41	1	2	yes	—
608	C₂×C₄×C₇	C₂×#41	1	2	yes	—
609	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
610	C₂²×Q₈	—	2	4	no	—
611	C₂²×Q₈	—	2	4	no	—
612	C₂²×Q₈	—	2	4	no	—
613	C₂²×Q₈	C₂³×C₇	1	2	yes	—
614	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
617	C₂²×D₄	C₂³×C₇	1	2	yes	—
618	C₂²×D₄	C₂³×C₇	1	2	yes	—
619	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₇	1	2	yes	—
621	C₂³×C₄	C₂³×C₇	1	2	yes	—
622	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
624	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₇	1	2	yes	—
626	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
629	#126	—	2	8	no	—
630	#125	—	2	4	no	—
631	#124	—	2	4	no	—
632	#124	—	2	4	no	—
633	#123	—	2	8	no	—
634	C₂²⋊Q₈	—	2	4	no	—
635	C₂²⋊Q₈	—	2	4	no	—
636	#121	—	2	8	no	—
637	#121	—	2	4	no	—
638	#121	—	2	4	no	—
639	C₄×Q₈	—	2	4	no	—
640	C₄×Q₈	—	2	4	no	—
641	C₄×Q₈	—	2	8	no	—
642	C₄×Q₈	—	2	4	no	—
643	C₄×Q₈	—	2	8	no	—
644	C₄×Q₈	C₇×D₄	1	8	yes	complemented
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	2	4	no	—
647	C₄×D₄	—	2	8	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	2	4	no	—
650	C₄×D₄	—	2	8	no	—
651	#117	—	2	8	no	—
652	C₂×C₄⋊C₄	—	2	4	no	—
653	C₂×C₄⋊C₄	—	2	8	no	—
654	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
696	C₂×C₄²	—	2	4	no	—
697	C₂×C₄²	—	2	8	no	—
698	C₂×C₄²	—	2	4	no	—
699	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₇	1	2	yes	—
704	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₇	1	2	yes	—
706	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₇	1	2	yes	—
709	C₂×C₄²	C₂³×C₇	1	2	yes	—
710	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₇	1	2	yes	—
716	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
717	#95	C₂³×C₇	1	2	yes	—
718	#95	C₂³×C₇	1	2	yes	—
719	#95	C₂³×C₇	1	2	yes	—
720	#95	C₂³×C₇	1	2	yes	—
721	#95	C₂³×C₇	1	1	yes	characteristic
722	#95	C₂³×C₇	1	1	yes	characteristic
723	#95	C₂³×C₇	1	1	yes	characteristic
724	#95	C₂³×C₇	1	1	yes	characteristic
725	#95	C₂³×C₇	1	1	yes	characteristic
726	#95	C₂³×C₇	1	1	yes	characteristic
727	#95	C₂³×C₇	1	2	yes	—
728	#95	C₂³×C₇	1	2	yes	—
729	#95	C₂³×C₇	1	2	yes	—
730	#95	C₂³×C₇	1	2	yes	—
731	#95	C₂³×C₇	1	2	yes	—
732	#95	C₂³×C₇	1	2	yes	—
733	#95	C₂³×C₇	1	2	yes	—
734	#95	C₂³×C₇	1	2	yes	—
735	#95	C₂³×C₇	1	2	yes	—
736	#95	C₂³×C₇	1	2	yes	—
737	#95	C₂³×C₇	1	2	yes	—
738	#95	C₂³×C₇	1	2	yes	—
739	#95	C₂³×C₇	1	2	yes	—
740	C₂²×C₇	—	2	2	no	—
741	C₂²×C₇	—	2	2	no	—
742	C₂²×C₇	—	2	2	no	—
743	C₂²×C₇	—	2	2	no	—
744	C₂²×C₇	—	2	2	no	—
745	C₂²×C₇	—	2	2	no	—
746	C₂²×C₇	—	2	2	no	—
747	C₂²×C₇	—	2	2	no	—
748	C₂²×C₇	—	2	2	no	—
749	C₂²×C₇	—	4	1	no	—
750	C₂²×C₇	—	4	1	no	—
751	C₂²×C₇	—	4	1	no	—
752	C₂²×C₇	—	4	1	no	—
753	C₂²×C₇	—	4	2	no	—
754	C₂²×C₇	—	4	2	no	—
755	C₂²×C₇	—	4	2	no	—
756	C₂²×C₇	—	4	2	no	—
757	C₂²×C₇	—	4	2	no	—
758	C₂²×C₇	—	4	2	no	—
759	C₂²×C₇	—	4	2	no	—
760	C₂²×C₇	#529	1	4	yes	complemented
761	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
762	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
763	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
764	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
765	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
766	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
767	C₂²×C₇	#585	1	1	yes	characteristic
768	C₄×C₇	—	2	4	no	—
769	C₄×C₇	—	2	4	no	—
770	C₄×C₇	—	2	2	no	—
771	C₄×C₇	—	2	2	no	—
772	C₄×C₇	—	2	2	no	—
773	C₄×C₇	—	2	2	no	—
774	C₄×C₇	—	2	4	no	—
775	C₄×C₇	—	4	1	no	—
776	C₄×C₇	—	4	2	no	—
777	C₄×C₇	—	4	1	no	—
778	C₄×C₇	—	4	1	no	—
779	C₄×C₇	—	4	2	no	—
780	C₄×C₇	—	4	1	no	—
781	C₄×C₇	—	4	2	no	—
782	C₄×C₇	—	4	1	no	—
783	C₄×C₇	—	4	1	no	—
784	C₄×C₇	—	4	2	no	—
785	C₄×C₇	—	4	1	no	—
786	C₄×C₇	#525	1	4	yes	—
787	C₄×C₇	#548	1	4	yes	—
788	C₂⁴	C₂⁴×C₇	1	2	yes	—
789	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
790	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
791	C₂×Q₈	—	2	32	no	—
792	C₂×Q₈	—	2	4	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	2	4	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
800	C₂×Q₈	C₇×#41	1	4	yes	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	4	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	C₇×#41	1	4	yes	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	4	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	4	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	C₇×#41	1	4	yes	—
839	C₂²×C₄	C₇×#41	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	4	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	4	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	4	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	4	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	4	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	4	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
880	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	2	4	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	4	no	—
905	C₄²	—	2	4	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	4	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	4	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	4	1	no	—
918	C₄²	C₂×C₇×D₄	1	4	yes	—
919	C₄²	C₂×C₇×D₄	1	8	yes	—
920	C₂×C₇	—	2	4	no	—
921	C₂×C₇	—	4	2	no	—
922	C₂×C₇	—	8	2	no	—
923	C₂×C₇	C₂×#525	1	1	yes	characteristic
924	C₂×C₇	C₂×#529	1	1	yes	characteristic
925	C₂×C₇	#3461	1	1	yes	characteristic
926	C₂×C₇	C₂×#548	1	1	yes	characteristic
927	C₂×C₇	D₄×#41	1	1	yes	characteristic
928	C₂×C₇	#3480	1	1	yes	characteristic
929	C₂×C₇	#3482	1	1	yes	characteristic
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	2	2	no	—
943	C₂³	—	2	2	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	C₂×C₇×#41	1	2	yes	—
948	C₂³	C₂×C₇×#41	1	2	yes	—
949	C₂³	C₂×C₇×#41	1	2	yes	—
950	C₂³	C₂×C₇×#41	1	2	yes	—
951	C₂³	C₂⁵×C₇	1	1	yes	characteristic
952	Q₈	—	2	16	no	—
953	Q₈	—	2	8	no	—
954	Q₈	—	2	8	no	—
955	D₄	—	2	8	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	4	no	—
959	C₂×C₄	—	2	16	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	8	no	—
975	C₂×C₄	—	2	8	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	4	no	—
1011	C₂×C₄	—	4	8	no	—
1012	C₂×C₄	—	4	4	no	—
1013	C₂×C₄	—	4	4	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1016	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
1017	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
1018	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1019	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1020	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1021	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1022	C₂×C₄	C₂×C₇×#41	1	4	yes	—
1023	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1024	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1025	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1026	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1027	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1028	C₇	#34708	1	1	yes	characteristic, direct product factor, Sylow
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	2	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	C₇×#529	1	4	yes	complemented
1050	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1051	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1052	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1053	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1054	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
1055	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1056	C₂²	C₇×#585	1	1	yes	characteristic
1057	C₄	—	2	4	no	—
1058	C₄	—	2	4	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	C₇×#525	1	4	yes	—
1076	C₄	C₇×#548	1	4	yes	—
1077	C₂	—	2	4	no	—
1078	C₂	—	4	2	no	—
1079	C₂	—	8	2	no	—
1080	C₂	C₂×C₇×#525	1	1	yes	characteristic
1081	C₂	C₂×C₇×#529	1	1	yes	characteristic
1082	C₂	C₇×#3461	1	1	yes	characteristic
1083	C₂	C₂×C₇×#548	1	1	yes	characteristic
1084	C₂	C₇×D₄×#41	1	1	yes	characteristic
1085	C₂	C₇×#3480	1	1	yes	characteristic
1086	C₂	C₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2416	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₂²×C₄×C₇×Q₈	C₂	semidirect
3. C₇×#2481	C₂	semidirect
4. C₇×#2469	C₂	semidirect
5. C₇×#2458	C₂	semidirect
6. C₇×#2453	C₂	semidirect
7. C₇×#2448	C₂	semidirect
8. C₇×#2443	C₂	semidirect
9. C₇×#2442	C₂	semidirect
10. C₇×#2436	C₂	semidirect
11. C₇×#2426	C₂	semidirect
12. C₇×#2421	C₂	semidirect
14. C₇×#2409	C₂	semidirect
15. C₇×#2398	C₂	semidirect
16. C₇×#2396	C₂	semidirect
17. C₄×C₇×#124	C₂	semidirect
18. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₇×#121	C₂	semidirect
20. C₄×C₇×#121	C₂	semidirect
21. C₇×#2295	C₂	semidirect
22. C₇×#2290	C₂	semidirect
23. C₄²×C₇×D₄	C₂	semidirect
125. #34708	C₇	direct (N × H)
160. C₄×C₇×Q₈	D₄	semidirect
256. C₂×#529	C₂×C₇	semidirect
257. C₂²×C₄×Q₈	C₂×C₇	semidirect
258. #2481	C₂×C₇	semidirect
259. #2469	C₂×C₇	semidirect
260. #2458	C₂×C₇	semidirect
261. #2453	C₂×C₇	semidirect
262. #2448	C₂×C₇	semidirect
263. #2443	C₂×C₇	semidirect
264. #2442	C₂×C₇	semidirect
265. #2436	C₂×C₇	semidirect
266. #2426	C₂×C₇	semidirect
267. #2421	C₂×C₇	semidirect
269. #2409	C₂×C₇	semidirect
270. #2398	C₂×C₇	semidirect
271. #2396	C₂×C₇	semidirect
272. C₄×#124	C₂×C₇	semidirect
273. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
274. C₄×#121	C₂×C₇	semidirect
275. C₄×#121	C₂×C₇	semidirect
276. #2295	C₂×C₇	semidirect
277. #2290	C₂×C₇	semidirect
278. C₄²×D₄	C₂×C₇	semidirect
644. C₄×Q₈	C₇×D₄	semidirect
760. C₂²×C₇	#529	semidirect
1028. C₇	#34708	direct (N × H)
1049. C₂²	C₇×#529	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#529	2
C₂²×C₄×C₇×Q₈	2
C₇×#2481	2
C₇×#2469	2
C₇×#2458	2
C₇×#2453	2
C₇×#2448	2
C₇×#2443	2
C₇×#2442	2
C₇×#2436	2
C₇×#2426	2
C₇×#2421	2
C₇×#2416	2
C₇×#2409	2
C₇×#2398	2
C₇×#2396	2
C₄×C₇×#124	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#121	2
C₇×#2295	2
C₇×#2290	2
C₄²×C₇×D₄	2
#34708	7

Subgroups — C7×#34708 #13211924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34708 #13211924